Carrier phase integer ambiguity resolution with inequality constraints for GPS and Galileo

Galileo and GPS receivers can measure the carrier phases with millimeter accuracy. However, the carrier phases are periodic which requires the resolution of an integer ambiguity for each satellite. This paper provides two new constrained integer least-squares estimators that include some a priori knowledge on the relative receiver position in spherical coordinates: a maximum a posteriori probability estimator and an inequality constrained integer ambiguity resolution. The latter one uses a polynomial barrier function. Both estimators enable a significant reduction of the integer search space, a substantial improvement in the float ambiguity estimates, and thereby, a higher probability of correct integer ambiguity resolution.